To calculate: The product of [x-(3-\sqrt{5})][x-(3+\sqrt{5})]

glamrockqueen7

glamrockqueen7

Answered question

2021-08-20

To calculate: The product of [x(35)][x(3+5)]

Answer & Explanation

Demi-Leigh Barrera

Demi-Leigh Barrera

Skilled2021-08-21Added 97 answers

Step 1
Formula used:
(a+b)(ab)=a2b2
(ab)2=a22ab+b2
Associative property, (a+b)+c=a+(b+c)
Step 2
If P (x) represent the given expression, then
P(x)=[x(35)][x(3+5)]
P(x)=(x3+5)(x35)
Use associative property of algebraic expressions,
Associative property is written as,
(a+b)+c=a+(b+c)
This property modifies the expression to,
P(x)=((x3)+5)((x3)5)
Apply arithmetic rule:
(a+b)(ab)=a2b2
Here, a=(x3), b=(5)
Hence,
P(x)=(x3)2(5)2Z
Apply arithmetic rule:
(ab)2=a22ab+b2
Here, a=x, b=3
Hence,
P(x)=(x3)2(5)2
=x26x+95
=x26x+4
Hence, the product of [x(35)][x(3+5)] is x26x+4
Jeffrey Jordon

Jeffrey Jordon

Expert2022-07-07Added 2605 answers

Answer is given below (on video)

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